Problem: Simplify the following expression: $z = \dfrac{x - 11}{8x + 4} - \dfrac{-3x - 18}{8x + 4}$
Answer: Since the expressions have the same denominator we simply subtract the numerators: $z = \dfrac{x - 11 - (-3x - 18)}{8x + 4}$ Distribute the negative sign: $z = \dfrac{x - 11 + 3x + 18}{8x + 4}$ Combine like terms: $z = \dfrac{4x + 7}{8x + 4}$